 New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  rabbiia GIF version

Theorem rabbiia 2849
 Description: Equivalent wff's yield equal restricted class abstractions (inference rule). (Contributed by NM, 22-May-1999.)
Hypothesis
Ref Expression
rabbiia.1 (x A → (φψ))
Assertion
Ref Expression
rabbiia {x A φ} = {x A ψ}

Proof of Theorem rabbiia
StepHypRef Expression
1 rabbiia.1 . . . 4 (x A → (φψ))
21pm5.32i 618 . . 3 ((x A φ) ↔ (x A ψ))
32abbii 2465 . 2 {x (x A φ)} = {x (x A ψ)}
4 df-rab 2623 . 2 {x A φ} = {x (x A φ)}
5 df-rab 2623 . 2 {x A ψ} = {x (x A ψ)}
63, 4, 53eqtr4i 2383 1 {x A φ} = {x A ψ}
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   = wceq 1642   ∈ wcel 1710  {cab 2339  {crab 2618 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-rab 2623 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator